Wait... Why are you trying to clean out all of the copper? Leave it in there! First, removing all of the copper exposes the rifling to faster wear. Second, the copper fills in some of the imperfections and smooths the bore. This is not some crazy rankings from a novice. Talk to Long-Range Tactical shooters and Snipers and they'll back me up. Don't be so quick to make that bore squeaky-clean after each range session. Let the bore get seasoned and broken-in. I, and many, many others, don't even clean our bolt guns until accuracy starts to fall off (often as many as 300-500 rounds). My bolt guns shoot 1/2MOA or better if I do my part.
Carbon fouling is something else. Clean the carbon from time to time if you're shooting with especially dirty powder. If my rifles have been sitting for more than a week or two I'll pull a bore-snake thru to wipe out the dust but that's about it.

Think of a car engine for a moment. Why do we use oil in the engine? To prevent metal-to-metal contact and reduce friction between two metal surfaces. Your barrel is no different from the engine. My instructions for barrel break-in were quite simple. Shoot 20 rounds (non-moly bullets) with no cleaning, as this will further burnish the barrel. Done! Now shoot and clean using your regular regimen of cleaning and if you have to use JB's or flitz type products, go very easy with them, or better yet avoid them. Never clean down to bare metal. Most of the cleaning products do a great job, don't be afraid to use a brush and go easy on the ammonia-based products for removing copper fouling. Basically don't let the ammonia-based products remain in the barrel for long lengths of time.

I use the foaming copper removel products, with very good results and HALF the cleaning time.
As to lapping, by removing the microscopic 'burrs', the barrel induces less friction and theoretically will last LONGER due to lower heat cycling and friction.
Lapped barrels last longer and are easier to clean, a win-win.